On a Bernoulli problem with geometric constraints

Antoine Laurain; Yannick Privat

ESAIM: Control, Optimisation and Calculus of Variations (2012)

  • Volume: 18, Issue: 1, page 157-180
  • ISSN: 1292-8119

Abstract

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A Bernoulli free boundary problem with geometrical constraints is studied. The domain Ω is constrained to lie in the half space determined by x1 ≥ 0 and its boundary to contain a segment of the hyperplane  {x1 = 0}  where non-homogeneous Dirichlet conditions are imposed. We are then looking for the solution of a partial differential equation satisfying a Dirichlet and a Neumann boundary condition simultaneously on the free boundary. The existence and uniqueness of a solution have already been addressed and this paper is devoted first to the study of geometric and asymptotic properties of the solution and then to the numerical treatment of the problem using a shape optimization formulation. The major difficulty and originality of this paper lies in the treatment of the geometric constraints.

How to cite

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Laurain, Antoine, and Privat, Yannick. "On a Bernoulli problem with geometric constraints." ESAIM: Control, Optimisation and Calculus of Variations 18.1 (2012): 157-180. <http://eudml.org/doc/221908>.

@article{Laurain2012,
abstract = {A Bernoulli free boundary problem with geometrical constraints is studied. The domain Ω is constrained to lie in the half space determined by x1 ≥ 0 and its boundary to contain a segment of the hyperplane  \{x1 = 0\}  where non-homogeneous Dirichlet conditions are imposed. We are then looking for the solution of a partial differential equation satisfying a Dirichlet and a Neumann boundary condition simultaneously on the free boundary. The existence and uniqueness of a solution have already been addressed and this paper is devoted first to the study of geometric and asymptotic properties of the solution and then to the numerical treatment of the problem using a shape optimization formulation. The major difficulty and originality of this paper lies in the treatment of the geometric constraints. },
author = {Laurain, Antoine, Privat, Yannick},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Free boundary problem; Bernoulli condition; shape optimization; free boundary problem},
language = {eng},
month = {2},
number = {1},
pages = {157-180},
publisher = {EDP Sciences},
title = {On a Bernoulli problem with geometric constraints},
url = {http://eudml.org/doc/221908},
volume = {18},
year = {2012},
}

TY - JOUR
AU - Laurain, Antoine
AU - Privat, Yannick
TI - On a Bernoulli problem with geometric constraints
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2012/2//
PB - EDP Sciences
VL - 18
IS - 1
SP - 157
EP - 180
AB - A Bernoulli free boundary problem with geometrical constraints is studied. The domain Ω is constrained to lie in the half space determined by x1 ≥ 0 and its boundary to contain a segment of the hyperplane  {x1 = 0}  where non-homogeneous Dirichlet conditions are imposed. We are then looking for the solution of a partial differential equation satisfying a Dirichlet and a Neumann boundary condition simultaneously on the free boundary. The existence and uniqueness of a solution have already been addressed and this paper is devoted first to the study of geometric and asymptotic properties of the solution and then to the numerical treatment of the problem using a shape optimization formulation. The major difficulty and originality of this paper lies in the treatment of the geometric constraints.
LA - eng
KW - Free boundary problem; Bernoulli condition; shape optimization; free boundary problem
UR - http://eudml.org/doc/221908
ER -

References

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